The wavelet transform and index theory
by
Dieter Klusch
FB Mathematik und Informatik, FU Berlin, Germany

The 1D-wavelet-transform with respect to Cauchy wavelets is used to deduce

• a wavelet calculus for complex power and exponential functions of self-adjoint operators in Hilbert spaces as well as
• a parameter-dependent index theory for Atiyah-Patodi-Singer operators on manifolds with boundary

Date received: August 9, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahz-86.